Question

Qual a solução da inequação I3x - 4I < 7? ​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Desigualdades~envolvendo~m\acute odulo}\\\sf\bigodot 1~|x|>a\iff x>a~ou~x>-a\\\sf\bigodot 2~|x|\geqslant a\iff x\geqslant a~ou~x\leqslant-a\\\sf\bigodot 3 ~|x|<a\iff -a<x<a\\\sf\bigodot 4~|x|\leqslant a\iff -a\leqslant x\leqslant a\end{array}}$

$\Large\boxed{\begin{array}{l}\sf |3x-4|<7 \\\sf-7<3x-4>7\\\sf -7+4>3x<7+4\\\sf -3<3x<11\\\\\sf-1<x<\dfrac{11}{3}\\\\\sf S=\bigg\{x\in\mathbb{R}/\!-1<x<\dfrac{11}{3}\bigg\}\end{array}}$